Nonclassical symmetry of nonlinear diffusion equation and factorization method |
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| Institution: | 1. Key Laboratory for Advanced Coal and Coking Technology of Liaoning Province, School of Chemical Engineering, University of Science and Technology Liaoning, Anshan 114051, China;2. Chemical Engineering, University of Newcastle, Callaghan, NSW 2308, Australia;3. SMART@UNSW, School of Materials Science & Engineering, University of New South Wales, Sydney 2052, Australia |
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| Abstract: | We present the nonclassical symmetry of a nonlinear diffusion equation whose a nonlinear term is an arbitrary function. Generally, there is no guarantee that we can always determine the nonclassical symmetries admitted by the given equation because of the nonlinearity included in the determining equations. Accordingly, constructing invariant solutions is also generally difficult. In this paper, we apply the factorization method to nonclassical symmetry analysis for the nonlinear diffusion equation. Applying this method simplifies the determining equations and leads to their invariant solution automatically. |
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